Intro to Higher Mathematics -- Spring 2016

MTH 300 - Intro to Higher Mathematics. A transition between elementary calculus and higher mathematics with emphasis on techniques of proof. (PR: C or better in MTH 230)

• Time and Place: 1:00 pm - 1:50 pm MTWR 509 Smith Hall
• Instructor: Peter Saveliev (call me Peter)
• Office: Smith Hall 713
• Office Hours: MW 2:30-4:45 (walk-in), or by appointment
• Office Phone: x4639
• E-mail: saveliev@marshall.edu
• Class Web-Page: math02.com
• Prerequisites: a certain level of mathematical maturity acquired through experience with calculus, algebra, geometry, etc.
• Text: How to read and do proofs by Solow
• Outcomes: the student will become proficient at reading proofs, checking proofs, discovering proofs, and writing proofs; the student will also start to become familiar with various constructions of advanced mathematics.
• Activities: the student will practice each outcome via the homework given in the textbook and online.
• Evaluation: the student achievement of each outcome will be assessed via
  • homework and quizzes: 40%
  • midterm: 25%
  • final exam: 35%

See also Course policy.

Lectures

Student's guide to proof writing

The lectures -- exactly as they appear in class -- will be linked here and updated on a daily basis:

• Set 1
• Set 2
• Set 3
• Set 4
• Set 5
• Set 6
• Set 7

• HW1

Chapters

• 1 The truth of it all 1
• 2 The forward-backward method 9
• 3 On definitions and mathematical terminology 23
• 4 Quantifiers I : the construction method 35
• 5 Quantifiers II : the choose method 45
• 6 Quantifiers III : specialization 59
• 7 Quantifiers IV : nested quantifiers 69
• 8 Nots of nots lead to knots 79
• 9 The contradiction method 87
• 10 The contrapositive method 99
• 11 Uniqueness methods and induction 107
• 12 Either/or and max/min methods 123
• 13 Summary 135

Notes

Upcoming:

• Intro to Higher Mathematics -- Spring 2016 -- midterm: Wednesday, March 9
• Intro to Higher Mathematics -- Spring 2016 -- final exam, Friday May 6, 12:45-2:45 pm, same place. (Note: If the two-hour time allowance results in a conflict in exam times, it is the student’s responsibility to notify the professor of the later course and to reschedule the later exam.)